I was wondering which transformations of dependent variable (y) are "allowed"? My problem is that I am trying to compare three groups (=categorical variable), basically to find out if the groups have significantly different y's. I cannot do this with any non-parametric test or the like, as this is a time series data so autocorrelation need to be considered (I'm using linear mixed model to fit the model). However, the y's are skewed in such a way that the residuals (either pooled or when checked by group) show a curved shape. If I had scale variables, I would try to use a model other than simple linear, but as I only have categoricals, this does not work. I have tried the "usual" transformations of y (log, 1/y, sqrt (y)), however none of these help. However, if I transform the y such as y'= (y+1)^-4, the residuals are ok. This seems kind of fishy for me, is this allowed? The cause for the skewedness of the data cannot be explained by anything that we measured, but I suspect there is some hidden factor explaining the "unexpected" high values of y.
I'm very thankful for any advice.